Krzysztof Lipiński

Dynamic Behaviour Comparison between Bogies : Rigid or Articulated Frame, Wheelset or Independent Wheels

The classical mathematical models and the corresponding multibody programs are not always adapted to the increasing diversity of railway bogie designs, since the most general envisaged case consists of a carbody (or several) carried by two rigid bogies equipped with wheelsets. Although the latter configuration still represents the major part of the railway vehicles in use, new concepts in the design of bogies (independent wheels, articulated frame, pneumatic suspensions,...) have a relatively poor scientific background with respect to the know-how gained in the domain of conventional vehicle : this justifies the development of more general mathematical modelling and computer programs, able to generate a reliable model in a relatively short time. The multibody program ROBOTRAN has been developed in that sense, offering the possibility to obtain the models of a family of railway vehicles - conventional or not - from a symbolic library of carbodies and bogies. The present paper illustates this through a comparison of behaviour between three bogies in a same situation :the entry curving at constant speed.

Mechanical engineering education via projects in multibody dynamics

The present contribution focuses on the feasibility and interest of setting up a multi‐disciplinary project in the field of multibody dynamics, as a sequel to the undergraduate course in classical mechanics. The pedagogical objectives of this “learning layer” cover various aspects, namely: give the student the opportunity to exploit and analyze the equations of motion for a real application, make them able to formulate consistent hypotheses for such applications and promote an actual multi‐disciplinary activity (mechanics, numerical methods, computer science and CAD). The project is performed by groups of students and is organized in the frame of a global active pedagogical process which characterizes our undergraduate engineering program at the Université catholique de Louvain (UCL, Belgium). After more than 10 years of experience, we can claim that this multi‐disciplinary project really improves the students skills in the field of multibody system modeling and computer simulation, including a timid but existing engineering attitude with respect to the results they obtain. Among the educational ingredients that make this project really fruitful educationally speaking, one must emphasize a key point of the approach, relating to the use of the symbolic multibody program ROBOTRAN to assist students in producing their equations of motion. Contrarily to research activities, the use of the ROBOTRAN symbolic models are exploited in such project, more for an educational motivation than for the computer efficiency of the simulation.

Redundantly Actuated 3RRR Parallel Planar Manipulator - Numerical Analyses of its Dynamics Sensitivity on Modifications of its Platforms Inertia Parameters

Below, numerical analyses, as well as dynamics of a complex mechanism, are presented. Two objectives are focused: inverse dynamic model is needed (dedicated to be use in the model predictive controller); an identification method is searched (some trajectory parameters are controlled, when specific trajectory is tracked under an open-loop model-based control), as selected parameters must be identified for the model. A redundantly actuated mechatronic system is considered (in the present case some planar, parallel manipulator). When the redundancies are present, traditional torque estimation techniques can not be used directly (a non-square matrix is present in the equations). Thus, the right Moore-Penrose pseudo-inverse is used to estimate them. To model the mechanism - multibody dynamics is used. Its dynamics equations are nonlinear in respect to the joints position (displacements are significant during the mechanism motion). An open-loop model-based control algorithm is postulated for the system (the subcomponents from the closed-loop controller will not be considered in the present paper). As the real parameters of the controlled object can differ from the ones proposed in the controller, obtained trajectories differ from the requested (open-loop controller is used only). Correlations between the inertia error and the trajectory errors are tested. Sensible trajectory parameters are searched to estimate inertia of the controlled object. At present, analyses are restricted to numerical experiments, only.

Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator

In the paper,numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator is driven over a larger operating range, nonlinear terms can be observed in the equations, and linear controller does not ensure satisfactory its performance. Thus, nonlinear control technique is employed. To ensure such non-linear control, nonlinear models of the plant are introduced in the controller. Initially, there is an open-loop feedforward model-based controller used to enforce the manipulator to follow the required paths. Work of the proposed configuration is tested numerically. To deal with it, a numerical model of the manipulator is prepared and rules of multibody modelling are used for it. Two identical models (equations) are implemented in two separate blocks of the model. In the controller block, primary set of parameters of the robot structure is introduced. As the actual gaol is to observe effects of the incorrect identification of the payload masses, the plant (the controlled object) model may not be described by identical values of their masses in the performed tests. As a result, significant path errors are observed during simulations. To eliminate these errors, the controller model is enlarged. A feedback loop is accepted and a proportional-derivative controller is considered in this feedback part. Subsequently, collaboration between these feedforward and feedback blocks is tested. This collaboration runs well (error of the realised path is reduced). However, intensive work of the feedback controller is non-required in the considered application. Possibility of mass identification is tested. Performed tests proofed that signal of the proportional-derivative controller is a useful data base for the required identification process. A short run of a trial path is performed at beginning of the motion. PD signal obtained during such test motion are collected. They allow us to identify the mass of the payload and to improve data in the model-based controller. Thanks of it, the feedback control signal is reduced and realisation of the required path is acceptable.

Numerical Model of Femur Part

The aim of the study is to create a new more accurate method of femur part modelling by using the finite element method. According to this new method, a femur part is treated as a complex structure composed of trabecular bone (internal part) and cortical bone (external part). The internal part is modelled as a scaffold, thus the external part is modelled as a coat (i.e. covering). Applying the programme ABAQUS, there were created four numerical models of trabecular femur part (regular shell bar-connected scaffold, regular solid bar-connected scaffold, irregular shell bar-connected scaffold, irregular solid bar-connected scaffold) and four numerical models of femur part composed of trabecular and cortical bone areas (regular shell bar-connected scaffold covered by shell coat, regular solid bar-connected scaffold covered by solid coat, irregular shell bar-connected scaffold covered by shell coat, irregular solid bar-connected scaffold covered by solid coat). Applying similar boundary conditions and similar load affected by muscles’ forces and external moments, presented numerical models had been tested. Considering stress (strain) fields obtained from numerical researches of presented models, there were drawn conclusions about influence of material nonlinearity and geometry nonlinearity and application of proposed new method in clinical biomechanics.

Rigid Finite Element Modeling for Identification of Vibrations in Elastic Rod Driven by a DC-Motor Supplied from a Thyristor Rectifier

The paper deals with the numerical analysis of electromechanical systems. The system consists of a DC motor supplied from a half-wave, single phase, thyristor rectifier, and of a flexible rod fixed to the axis of armature. Discretization of rigid segments is used to model flexibility of the rod. The discrete structure is considered as a multibody system, i.e. as a single kinematical chain of rigid bodies connected by massless joints. Significant drift rotation is included in the rod model. Numerical integration is performed in order to predict behavior of the system. Two working conditions are tested: steady-state motion and transient braking of the system. The attention in the paper is concentrated on interactions between the mechanical and electrical systems.

Limb/Ground Impacts and Unexpected Impacts Control Strategy for a Model of a Walking Robot Limb

The paper deals with numerical analysis of dynamics of walking robots. The focus is on limb/ground contact. Normal and tangent direction are considered separately. In the normal one, the contacts are modeled as unilateral constraints. In the tangent one, slip and friction are considered. As the contacts are unilateral, nonzero velocities could be present before the contact. These velocities diminish rapidly, and significant contact forces are present. The forces have destructive influence on the robot structure, and the impulsive changes of the arms velocities can disorient the control system. In the paper, the impact consequences are discussed, as well as consequences of installation of a 0/1 contact sensor. A 3D mechatronic multibody model of a quote of a robot is considered. Its limb is driven by DC motors and controlled by a dedicated control system. With the zero signals from the sensor, the control prevents a constant velocity of the limb end. The normal component of the velocity has to be stopped at the positive signals, and the motor current has to be reduced. Exemplary calculations are presented in the paper.

Multibody and Electromechanical Modelling in Dynamic Balancing of Mechanisms for Mechanical and Electromechanical Systems

The paper focuses on dynamics of an electromechanical system composed of a DC motor and a planar four-bar mechanism. Minimization of mechanism/frame interactions is considered. Simultaneous elimination of frame shaking forces and torques is requested. The employed balancing method is counterweights allocation. Their parameters are found with a numerical modelling and a numerical optimization. They depend on shape of the mechanism’s velocity. Three alternative drives are tested in the paper: constant velocity drive; constant torque drive; and DC motor. The optimal counterweight’s parameters are derived for all these drives. Obtained results approved necessity of precise electromechanical modelling.

Some really simple but useful model of substitutable elasticity modelled as elasticity in six subsequent joints

The paper devotes its attention to an analysis of dynamics of multibody systems. We assumed as evident that any rigid bodies’ multibody structure could be modelled easily, as a big number of methodologies exist and their descriptions are present in the literature from years. Thus the actual challenge is not a new methodology. The challenge is the effective way of modelling. At this same time, there is not any unique and universal method of modelling. For most of real structures, they can be modelled using few alternative sequences of bodies. Moreover, within the structures we can easily locate some specific substructures that can be modelled with the general, classical methodology or by some shorter algorithm dedicated to these specific substructures. We will focus on one of such substructures. The detail is an elastic support of a rigid body. If motions of such body are small one of the most popular model is an elasticity formula with nonzero diagonal elasticity coefficients. The model of the spring with diagonal matrix becomes inoperative if someone considers significant displacements of the body. Then some alternative could be the concept of elasticity present in six subsequent joints of massless multibody structure. It can be modelled as a closed loop substructure, or as some direct analytical formula. The second is numerically shorter and more effective. However, its equations are not intuitive, and thus it looks interesting to present them in a separate paper. The detail is extracted from the multibody structure and is presented.

Optimal dampers localization for a body under double load and the body behaviour for its intermediate loads

A multibody dynamics is a well-known tool used in many analyses of mechanisms. It simplifies predictions of any mechanism behaviour, even in long before of time when the final mechanism is set to any physical experiment. Some important step in a project preparation is a selection of elastic and damping coefficients for elements of the system. The process can be simplified if a combination of dynamics and optimisation tools is in a disposition of project manager. But even then, it request in a numbers of numerical calculation, so numerically effective models are necessary. The paper presents researches in an optimal configuration of damping elements. In some previous, publication [2] we had focus on question: whether it is possible to obtain a configuration of dampers that satisfy presumed level of damping of vibrations for a structure with varying load Especially, does exist it for a single body with double sets of workload. The answer was negative, even if some important improvement of damping was obtained. Within the actual paper some deeper analyse of behaviour of the optimised system is performed, especially its behaviour for intermediate loads is analysed. Short description of rigid bodies multibody dynamics